What is the death? Physically? Or spiritually? A gentile who abstains from melacha is liable to death as it says "day and night they shall not stop" (sanhedrin 58b)
This is discussed in the Gemara in Sanhedrein 58b-59a
Basically, if Gentiles keep Shabbat they cannot be put to death since they didn't do anything - and we never kill people for not doing something.
So it must mean some type of heavenly punishment.